Is it permissible or forbidden to take a percentage of the amounts paid for processing transactions, without the knowledge of the first party?

It appears that collecting transactions from their owners is considered a form of ijarah (leasing/hiring). Thus, there is no harm in entrusting them to someone else to complete for less than what you received for them. It is not a condition for that person to know whether or not you are receiving a fee for them. Therefore, you are permitted to hire someone else, unless it was stipulated that you must perform the work yourself.